Nonlinear analysis of laminated FG-GPLRC beams resting on an elastic foundation based on the two-phase stress-driven nonlocal model

2021 ◽  
Author(s):  
R. Ansari ◽  
M. Faraji Oskouie ◽  
M. Roghani ◽  
H. Rouhi
Keyword(s):  
Nonlinear Analysis ◽  
Elastic Foundation ◽  
Nonlocal Model ◽  
Two Phase

Exact solutions for the bending of Timoshenko beams using Eringen’s two-phase nonlocal model

2018 ◽  
Vol 24 (3) ◽  
pp. 559-572 ◽  
Author(s):  
Yuanbin Wang ◽  
Kai Huang ◽  
Xiaowu Zhu ◽  
Zhimei Lou
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Model ◽  
Bernoulli Beam ◽  
Two Phase ◽  
Differential Model ◽  
Euler Bernoulli Beam

Eringen’s nonlocal differential model has been widely used in the literature to predict the size effect in nanostructures. However, this model often gives rise to paradoxes, such as the cantilever beam under end-point loading. Recent studies of the nonlocal integral models based on Euler–Bernoulli beam theory overcome the aforementioned inconsistency. In this paper, we carry out an analytical study of the bending problem based on Eringen’s two-phase nonlocal model and Timoshenko beam theory, which accounts for a better representation of the bending behavior of short, stubby nanobeams where the nonlocal effect and transverse shear deformation are significant. The governing equations are established by the principal of virtual work, which turns out to be a system of integro-differential equations. With the help of a reduction method, the complicated system is reduced to a system of differential equations with mixed boundary conditions. After some detailed calculations, exact analytical solutions are obtained explicitly for four types of boundary conditions. Asymptotic analysis of the exact solutions reveals clearly that the nonlocal parameter has the effect of increasing the deflections. In addition, as compared with nonlocal Euler–Bernoulli beam, the shear effect is evident, and an additional scale effect is captured, indicating the importance of applying higher-order beam theories in the analysis of nanostructures.

Investigation on the effect of polymer in vertical oil-water two-phase flow using nonlinear analysis

2017 ◽  
Vol 80 ◽  
pp. 1-18 ◽  
Author(s):  
Q.Y. Yang ◽  
Y.F. Han ◽  
W.X. Liu ◽  
H.X. Zhang ◽  
Y.Y. Ren ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Oil Water

scholarly journals The nonlinear analysis of horizontal oil-water two-phase flow in a small diameter pipe

2017 ◽  
Vol 92 ◽  
pp. 39-49 ◽  
Author(s):  
Lu-Sheng Zhai ◽  
Panagiota Angeli ◽  
Ning-De Jin ◽  
Da-Shi Zhou ◽  
Lei Zhu
Keyword(s):  
Nonlinear Analysis ◽  
Two Phase Flow ◽  
Small Diameter ◽  
Phase Flow ◽  
Two Phase ◽  
Diameter Pipe ◽  
Oil Water
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